Thermodynamic Properties of the Two-Dimensional Coulomb Gas in the Low-Density Limit

TL;DR

This paper derives the leading correction to the thermodynamics of a two-dimensional Coulomb gas with hard-core particles, extending the exact low-density results to higher inverse temperatures and confirming the behavior near the collapse point through simulations.

Contribution

It provides the first correction to the thermodynamics of the 2D Coulomb gas with finite particle size, extending the exact results to a broader temperature range.

Findings

Correctly reproduces singularities at the collapse point β=2

Extends thermodynamic analysis to 2 ≤ β < 3

Agrees well with Monte-Carlo simulation results

Abstract

The model under consideration is the two-dimensional Coulomb gas of $\pm$ charged hard disks with diameter $\sigma$. For the case of pointlike charges $(\sigma=0)$, the system is stable against collapse of positive-negative pairs of charges in the range of inverse temperatures $0 \le \beta < 2$, where its full thermodynamics was obtained exactly [L. {\v{S}}amaj and I. Trav{\v{e}}nec, {\it J. Stat. Phys.} {\bf 101}:713 (2000)]. In the present work, we derive the leading correction to the exact thermodynamics of pointlike charges due to the presence of the hard core $\sigma$ (appearing in the dimensionless combination $n\sigma^2$, $n$ is the particle density). This permits us to extend the treatment to the interval $2\le \beta <3$ (the Kosterlitz-Thouless phase transition takes place at $\beta=4$). The results, which are exact in the low-density limit $n\sigma^2 \to 0$, reproduce correctly the singularities of thermodynamic quantities at the collapse point $\beta=2$ and agree very well with Monte-Carlo simulations.